Highest Common Factor of 632, 996, 686 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 632, 996, 686 i.e. 2 the largest integer that leaves a remainder zero for all numbers.
HCF of 632, 996, 686 is 2 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 632, 996, 686 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 632, 996, 686 is 2.
HCF(632, 996, 686) = 2
HCF of 632, 996, 686 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 632, 996, 686 is 2.
Highest Common Factor of 632,996,686 is 2
Step 1: Since 996 > 632, we apply the division lemma to 996 and 632, to get
996 = 632 x 1 + 364
Step 2: Since the reminder 632 ≠ 0, we apply division lemma to 364 and 632, to get
632 = 364 x 1 + 268
Step 3: We consider the new divisor 364 and the new remainder 268, and apply the division lemma to get
364 = 268 x 1 + 96
We consider the new divisor 268 and the new remainder 96,and apply the division lemma to get
268 = 96 x 2 + 76
We consider the new divisor 96 and the new remainder 76,and apply the division lemma to get
96 = 76 x 1 + 20
We consider the new divisor 76 and the new remainder 20,and apply the division lemma to get
76 = 20 x 3 + 16
We consider the new divisor 20 and the new remainder 16,and apply the division lemma to get
20 = 16 x 1 + 4
We consider the new divisor 16 and the new remainder 4,and apply the division lemma to get
16 = 4 x 4 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 4, the HCF of 632 and 996 is 4
Notice that 4 = HCF(16,4) = HCF(20,16) = HCF(76,20) = HCF(96,76) = HCF(268,96) = HCF(364,268) = HCF(632,364) = HCF(996,632) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 686 > 4, we apply the division lemma to 686 and 4, to get
686 = 4 x 171 + 2
Step 2: Since the reminder 4 ≠ 0, we apply division lemma to 2 and 4, to get
4 = 2 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 2, the HCF of 4 and 686 is 2
Notice that 2 = HCF(4,2) = HCF(686,4) .
HCF using Euclid's Algorithm Calculation Examples
Here are some samples of HCF using Euclid's Algorithm calculations.
Frequently Asked Questions on HCF of 632, 996, 686 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 632, 996, 686?
Answer: HCF of 632, 996, 686 is 2 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 632, 996, 686 using Euclid's Algorithm?
Answer: For arbitrary numbers 632, 996, 686 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.